Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Application of New Orthogonal Shifted Vieta-Lucas Polynomials in Solving Integro-Differential Equations: Methods and Results

Mohsen Riahi Beni
Iranian Journal of Science (2025)
https://doi.org/10.1007/s40995-024-01774-x

Uniform error analysis of an exponential IMEX-SAV method for the incompressible flows with large Reynolds number based on grad-div stabilization

Rong An and Weiwen Wan
Communications in Nonlinear Science and Numerical Simulation 140 108386 (2025)
https://doi.org/10.1016/j.cnsns.2024.108386

A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization

Lisa Davis, Monika Neda, Faranak Pahlevani, Jorge Reyes and Jiajia Waters
Computational Methods in Applied Mathematics 25 (1) 77 (2025)
https://doi.org/10.1515/cmam-2023-0222

Efficient fully discrete and decoupled scheme with unconditional energy stability and second-order accuracy for micropolar Navier–Stokes equations

Guo-Dong Zhang, Yunqing Huang, Xiaoming He and Xiaofeng Yang
Computer Methods in Applied Mechanics and Engineering 436 117692 (2025)
https://doi.org/10.1016/j.cma.2024.117692

Continuous interior penalty stabilization for divergence-free finite element methods

Gabriel R Barrenechea, Erik Burman, Ernesto Cáceres and Johnny Guzmán
IMA Journal of Numerical Analysis 44 (2) 980 (2024)
https://doi.org/10.1093/imanum/drad030

A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions

Bo Zheng and Yueqiang Shang
Advances in Computational Mathematics 50 (1) (2024)
https://doi.org/10.1007/s10444-023-10101-8

On Generalized Preconditioners for Time-Parallel Parabolic Optimal Control

Arne Bouillon, Giovanni Samaey and Karl Meerbergen
SIAM Journal on Scientific Computing 46 (4) A2298 (2024)
https://doi.org/10.1137/23M1553194

Convergence analysis of Euler and BDF2 grad-div stabilization methods for the time-dependent penetrative convection model

Weiwen Wan and Rong An
AIMS Mathematics 9 (1) 453 (2024)
https://doi.org/10.3934/math.2024025

Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation

Soheil Firooz, B. Daya Reddy, Vasily Zaburdaev and Paul Steinmann
Computer Methods in Applied Mechanics and Engineering 419 116649 (2024)
https://doi.org/10.1016/j.cma.2023.116649

An efficient variational multiscale element free Galerkin method based on adaptive TR-AB2 scheme for convection–diffusion equations

Xiaohua Zhang and Shuyi Xiang
Engineering Analysis with Boundary Elements 158 211 (2024)
https://doi.org/10.1016/j.enganabound.2023.10.026

Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem

Satyajith Bommana Boyana, Thomas Lewis, Sijing Liu and Yi Zhang
Computers & Mathematics with Applications 175 224 (2024)
https://doi.org/10.1016/j.camwa.2024.09.027

Partitioned schemes for the blood solute dynamics model by the variational multiscale method

Yongshuai Wang, Zhenjiang Peng, Md. Abdullah Al Mahbub and Haibiao Zheng
Applied Numerical Mathematics (2024)
https://doi.org/10.1016/j.apnum.2024.01.006

A Lagrange interpolation with preprocessing to nearly eliminate oscillations

Bernardo de la Calle Ysern and Pedro Galán del Sastre
Numerical Algorithms 97 (4) 2051 (2024)
https://doi.org/10.1007/s11075-024-01778-z

Solving incompressible Navier-Stokes equations: A nonlinear multiscale approach

Riedson Baptista, Isaac P. dos Santos and Lucia Catabriga
Computers & Mathematics with Applications 175 366 (2024)
https://doi.org/10.1016/j.camwa.2024.10.009

A nodally bound-preserving finite element method for reaction–convection–diffusion equations

Abdolreza Amiri, Gabriel R. Barrenechea and Tristan Pryer
Mathematical Models and Methods in Applied Sciences 34 (08) 1533 (2024)
https://doi.org/10.1142/S0218202524500283

Stabilized isogeometric collocation methods for scalar transport and incompressible fluid flow

Ryan M. Aronson, Corey Wetterer-Nelson and John A. Evans
Computer Methods in Applied Mechanics and Engineering 417 116283 (2023)
https://doi.org/10.1016/j.cma.2023.116283

An Lp-primal–dual finite element method for first-order transport problems

Dan Li, Chunmei Wang and Junping Wang
Journal of Computational and Applied Mathematics 434 115345 (2023)
https://doi.org/10.1016/j.cam.2023.115345

Maximum norm a posteriori error estimates for convection–diffusion problems

Alan Demlow, Sebastian Franz and Natalia Kopteva
IMA Journal of Numerical Analysis 43 (5) 2562 (2023)
https://doi.org/10.1093/imanum/drad001

Adaptive stabilized finite elements via residual minimization onto bubble enrichments

Jose G. Hasbani, Paulina Sepúlveda, Ignacio Muga, Victor M. Calo and Sergio Rojas
Computers & Mathematics with Applications 151 1 (2023)
https://doi.org/10.1016/j.camwa.2023.09.010

Implicit-Explicit Time Discretization for Oseen’s Equation at High Reynolds Number with Application to Fractional Step Methods

Erik Burman, Deepika Garg and Johnny Guzman
SIAM Journal on Numerical Analysis 61 (6) 2859 (2023)
https://doi.org/10.1137/23M1547573

On numerical simulation of fluid - structure interaction problems using variational multiscale methods

Petr Sváček
Journal of Computational and Applied Mathematics 427 115125 (2023)
https://doi.org/10.1016/j.cam.2023.115125

Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

Volker John, Baptiste Moreau and Julia Novo
Computers & Mathematics with Applications 122 48 (2022)
https://doi.org/10.1016/j.camwa.2022.07.017

Recent Advances in Mechanics and Fluid-Structure Interaction with Applications

William Snyder, Changhong Mou, Honghu Liu, et al.
Advances in Mathematical Fluid Mechanics, Recent Advances in Mechanics and Fluid-Structure Interaction with Applications 167 (2022)
https://doi.org/10.1007/978-3-031-14324-3_8

Fast rotated BSOR method for block two-by-two linear systems with application to PDE-constrained optimal control problems

Zhao-Zheng Liang and Yan Dou
BIT Numerical Mathematics 62 (4) 1175 (2022)
https://doi.org/10.1007/s10543-022-00908-0

A nearly-conservative, high-order, forward Lagrange–Galerkin method for the resolution of compressible flows on unstructured triangular meshes

Manuel Colera, Jaime Carpio and Rodolfo Bermejo
Journal of Computational Physics 467 111471 (2022)
https://doi.org/10.1016/j.jcp.2022.111471

Stabilizing the convection–diffusion–reaction equation via local problems

Utku Kaya and Malte Braack
Computer Methods in Applied Mechanics and Engineering 398 115243 (2022)
https://doi.org/10.1016/j.cma.2022.115243

A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations

Yueqiang Shang and Qihui Zhang
Discrete & Continuous Dynamical Systems - B 26 (6) 3119 (2021)
https://doi.org/10.3934/dcdsb.2020222

Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction

Mustafa Aggul and Songül Kaya
Applied Numerical Mathematics 160 178 (2021)
https://doi.org/10.1016/j.apnum.2020.10.004

Convergence analysis of a new dynamic diffusion method

Isaac P. Santos, Sandra M.C. Malta, Andrea M.P. Valli, Lucia Catabriga and Regina C. Almeida
Computers & Mathematics with Applications 98 1 (2021)
https://doi.org/10.1016/j.camwa.2021.06.012

A nearly-conservative, high-order, forward Lagrange–Galerkin method for the resolution of scalar hyperbolic conservation laws

Manuel Colera, Jaime Carpio and Rodolfo Bermejo
Computer Methods in Applied Mechanics and Engineering 376 113654 (2021)
https://doi.org/10.1016/j.cma.2020.113654

On the convergence order of the finite element error in the kinetic energy for high Reynolds number incompressible flows

Bosco García-Archilla, Volker John and Julia Novo
Computer Methods in Applied Mechanics and Engineering 385 114032 (2021)
https://doi.org/10.1016/j.cma.2021.114032

A stabilized local projection finite element scheme for computations of oldroyd-B viscoelastic fluid flows

Shweta Srivastava and Sashikumaar Ganesan
International Journal of Advances in Engineering Sciences and Applied Mathematics 13 (4) 383 (2021)
https://doi.org/10.1007/s12572-022-00314-3

Computational Science and Its Applications – ICCSA 2021

Andrea M. P. Valli, Isaac P. Santos, Sandra M. C. Malta, Lucia Catabriga and Regina C. Almeida
Lecture Notes in Computer Science, Computational Science and Its Applications – ICCSA 2021 12949 48 (2021)
https://doi.org/10.1007/978-3-030-86653-2_4

Variational multiscale virtual element method for the convection-dominated diffusion problem

Cong Xie, Gang Wang and Xinlong Feng
Applied Mathematics Letters 117 107077 (2021)
https://doi.org/10.1016/j.aml.2021.107077

A posteriori error estimation and adaptivity based on VMS for the incompressible Navier–Stokes equations

Diego Irisarri and Guillermo Hauke
Computer Methods in Applied Mechanics and Engineering 373 113508 (2021)
https://doi.org/10.1016/j.cma.2020.113508

A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

Roberto J. Cier, Sergio Rojas and Victor M. Calo
Mechanics Research Communications 112 103602 (2021)
https://doi.org/10.1016/j.mechrescom.2020.103602

Adaptive hybridizable discontinuous Galerkin methods for nonstationary convection diffusion problems

Haitao Leng and Yanping Chen
Advances in Computational Mathematics 46 (4) (2020)
https://doi.org/10.1007/s10444-020-09795-x

An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

Victor M. Calo, Alexandre Ern, Ignacio Muga and Sergio Rojas
Computer Methods in Applied Mechanics and Engineering 363 112891 (2020)
https://doi.org/10.1016/j.cma.2020.112891

A projection based variational multiscale method for a fluid–fluid interaction problem

Mustafa Aggul, Fatma G. Eroglu, Songül Kaya and Alexander E. Labovsky
Computer Methods in Applied Mechanics and Engineering 365 112957 (2020)
https://doi.org/10.1016/j.cma.2020.112957

Computational Science and Its Applications – ICCSA 2020

Ramoni Z. S. Azevedo and Isaac P. Santos
Lecture Notes in Computer Science, Computational Science and Its Applications – ICCSA 2020 12251 455 (2020)
https://doi.org/10.1007/978-3-030-58808-3_33

Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains

Shweta Srivastava and Sashikumaar Ganesan
BIT Numerical Mathematics 60 (2) 481 (2020)
https://doi.org/10.1007/s10543-019-00783-2

An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows

Medine Demir and Songül Kaya
Applied Numerical Mathematics 156 140 (2020)
https://doi.org/10.1016/j.apnum.2020.04.010

An assessment of two classes of variational multiscale methods for the simulation of incompressible turbulent flows

Naveed Ahmed and Volker John
Computer Methods in Applied Mechanics and Engineering 365 112997 (2020)
https://doi.org/10.1016/j.cma.2020.112997

Primal Dual Mixed Finite Element Methods for Indefinite Advection-Diffusion Equations

Erik Burman and Cuiyu He
SIAM Journal on Numerical Analysis 57 (6) 2785 (2019)
https://doi.org/10.1137/18M1221473

The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach Spaces

Ignacio Muga, Matthew J. W. Tyler and Kristoffer G. van der Zee
Computational Methods in Applied Mathematics 19 (3) 557 (2019)
https://doi.org/10.1515/cmam-2018-0199

Recent Developments in Variational Multiscale Methods for Large-Eddy Simulation of Turbulent Flow

Ursula Rasthofer and Volker Gravemeier
Archives of Computational Methods in Engineering 25 (3) 647 (2018)
https://doi.org/10.1007/s11831-017-9209-4

Variational multiscale modeling with discontinuous subscales: analysis and application to scalar transport

Christopher Coley and John A. Evans
Meccanica 53 (6) 1241 (2018)
https://doi.org/10.1007/s11012-017-0786-y

A parameter-free dynamic diffusion method for advection–diffusion–reaction problems

Andrea M.P. Valli, Regina C. Almeida, Isaac P. Santos, et al.
Computers & Mathematics with Applications 75 (1) 307 (2018)
https://doi.org/10.1016/j.camwa.2017.09.020

Two-level finite element variational multiscale method based on bubble functions for the steady incompressible MHD flow

Tong Zhang, Yanxia Qian and YuGao HuangFu
International Journal of Computer Mathematics 94 (3) 515 (2017)
https://doi.org/10.1080/00207160.2015.1115023

Defect-correction finite element method based on Crank-Nicolson extrapolation scheme for the transient conduction-convection problem with high Reynolds number

Haiyan Su, Xinlong Feng and Yinnian He
International Communications in Heat and Mass Transfer 81 229 (2017)
https://doi.org/10.1016/j.icheatmasstransfer.2016.12.014

A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

Naveed Ahmed, Tomás Chacón Rebollo, Volker John and Samuele Rubino
Archives of Computational Methods in Engineering 24 (1) 115 (2017)
https://doi.org/10.1007/s11831-015-9161-0

Convergence to Suitable Weak Solutions for a Finite Element Approximation of the Navier–Stokes Equations with Numerical Subgrid Scale Modeling

Santiago Badia and Juan Vicente Gutiérrez-Santacreu
Journal of Scientific Computing 71 (1) 386 (2017)
https://doi.org/10.1007/s10915-016-0304-8

A Multilevel Finite Element Variational Multiscale Method for Incompressible Navier‐Stokes Equations Based on Two Local Gauss Integrations

Yamiao Zhang, Biwu Huang, Jiazhong Zhang, Zexia Zhang and Xesús Nogueira
Mathematical Problems in Engineering 2017 (1) (2017)
https://doi.org/10.1155/2017/4917054

Blending low-order stabilised finite element methods: A positivity-preserving local projection method for the convection–diffusion equation

Gabriel R. Barrenechea, Erik Burman and Fotini Karakatsani
Computer Methods in Applied Mechanics and Engineering 317 1169 (2017)
https://doi.org/10.1016/j.cma.2017.01.016

Projection stabilized nonconforming finite element methods for the stokes problem

Boujemâa Achchab, Abdellatif Agouzal, Khalid Bouihat, Adil Majdoubi and Ali Souissi
Numerical Methods for Partial Differential Equations 33 (1) 218 (2017)
https://doi.org/10.1002/num.22083

A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows

Fatma G. Eroglu, Songul Kaya and Leo G. Rebholz
Computer Methods in Applied Mechanics and Engineering 325 350 (2017)
https://doi.org/10.1016/j.cma.2017.07.017

Second order fully discrete defect‐correction scheme for nonstationary conduction‐convection problem at high Reynolds number

Haiyan Su, Xinlong Feng and Yinnian He
Numerical Methods for Partial Differential Equations 33 (3) 681 (2017)
https://doi.org/10.1002/num.22115

Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues

A. Ern and J.-L. Guermond
Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues 17 265 (2016)
https://doi.org/10.1016/bs.hna.2016.09.017

Fluid dynamic design of an axial rotor for hydrokinetic riverbed turbine‐improvement introduced by a high lift foil profile

Sergio A. Oller, Liz G. Nallim and Sergio Oller
Environmental Progress & Sustainable Energy 35 (4) 1198 (2016)
https://doi.org/10.1002/ep.12320

Two-grid variational multiscale method with bubble stabilization for convection diffusion equation

Zhifeng Weng, Jerry Zhijian Yang and Xiliang Lu
Applied Mathematical Modelling 40 (2) 1097 (2016)
https://doi.org/10.1016/j.apm.2015.06.023

A second order in time local projection stabilized Lagrange–Galerkin method for Navier–Stokes equations at high Reynolds numbers

R. Bermejo and L. Saavedra
Computers & Mathematics with Applications 72 (4) 820 (2016)
https://doi.org/10.1016/j.camwa.2016.05.012

Finite Element Methods for Incompressible Flow Problems

Volker John
Springer Series in Computational Mathematics, Finite Element Methods for Incompressible Flow Problems 51 447 (2016)
https://doi.org/10.1007/978-3-319-45750-5_8

Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

An Liu, Yuan Li and Rong An
Advances in Applied Mathematics and Mechanics 8 (6) 932 (2016)
https://doi.org/10.4208/aamm.2014.m595

A vertex-based scheme on polyhedral meshes for advection–reaction equations with sub-mesh stabilization

Pierre Cantin, Jérôme Bonelle, Erik Burman and Alexandre Ern
Computers & Mathematics with Applications 72 (9) 2057 (2016)
https://doi.org/10.1016/j.camwa.2016.07.038

Error estimation for low-order adaptive finite element approximations for fluid flow problems

Alejandro Allendes, Francisco Durán and Richard Rankin
IMA Journal of Numerical Analysis 36 (4) 1715 (2016)
https://doi.org/10.1093/imanum/drv031

TWO-LEVEL ITERATION PENALTY AND VARIATIONAL MULTISCALE METHOD FOR STEADY INCOMPRESSIBLE FLOWS

Yuqing Zhang, Yuan Li and Rong An
Journal of Applied Analysis & Computation 6 (3) 607 (2016)
https://doi.org/10.11948/2016042

Local CIP Stabilization for Composite Finite Elements

Erik Burman and Friedhelm Schieweck
SIAM Journal on Numerical Analysis 54 (3) 1967 (2016)
https://doi.org/10.1137/15M1039390

Two-level variational multiscale finite element methods for Navier–Stokes type variational inequality problem

Yuan Li and Rong An
Journal of Computational and Applied Mathematics 290 656 (2015)
https://doi.org/10.1016/j.cam.2015.06.018

SUPG reduced order models for convection-dominated convection–diffusion–reaction equations

Swetlana Giere, Traian Iliescu, Volker John and David Wells
Computer Methods in Applied Mechanics and Engineering 289 454 (2015)
https://doi.org/10.1016/j.cma.2015.01.020

A Characteristics-Mix Stabilized Finite Element Method for Variable Density Incompressible Navier-Stokes Equations

Fei Xiong, Liquan Mei, Ying Li and Wu Zhang
Advances in Pure Mathematics 05 (05) 251 (2015)
https://doi.org/10.4236/apm.2015.55026

Nonlocal convection–diffusion problems and finite element approximations

Hao Tian, Lili Ju and Qiang Du
Computer Methods in Applied Mechanics and Engineering 289 60 (2015)
https://doi.org/10.1016/j.cma.2015.02.008

Robusta posteriorierror estimates for stabilized finite element methods

L. Tobiska and R. Verfürth
IMA Journal of Numerical Analysis 35 (4) 1652 (2015)
https://doi.org/10.1093/imanum/dru060

Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection–diffusion problems

Jikun Zhao, Shaochun Chen, Bei Zhang and Shipeng Mao
Applied Mathematics and Computation 264 346 (2015)
https://doi.org/10.1016/j.amc.2015.04.091

Sensitivity Analysis and Computations of the Time Relaxation Model

Monika Neda, Fran Pahlevani and Jiajia Waters
Advances in Applied Mathematics and Mechanics 7 (1) 89 (2015)
https://doi.org/10.4208/aamm.2013.m296

Mixed stabilized finite element methods based on backward difference/Adams–Bashforth scheme for the time-dependent variable density incompressible flows

Ying Li, Jian Li, Liquan Mei and Yingping Li
Computers & Mathematics with Applications 70 (10) 2575 (2015)
https://doi.org/10.1016/j.camwa.2015.09.021

A Stabilized Galerkin Scheme for the Convection-Diffusion-Reaction Equations

Qingfang Liu, Yanren Hou, Lei Ding and Qingchang Liu
Acta Applicandae Mathematicae 130 (1) 115 (2014)
https://doi.org/10.1007/s10440-013-9840-5

Robust error estimates in weak norms for advection dominated transport problems with rough data

Erik Burman
Mathematical Models and Methods in Applied Sciences 24 (13) 2663 (2014)
https://doi.org/10.1142/S021820251450033X

Error analysis of a fully discrete finite element variational multiscale method for the natural convection problem

Yunzhang Zhang, Yanren Hou and Jianping Zhao
Computers & Mathematics with Applications 68 (4) 543 (2014)
https://doi.org/10.1016/j.camwa.2014.06.008

Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part II: Hyperbolic Equations

Erik Burman
SIAM Journal on Scientific Computing 36 (4) A1911 (2014)
https://doi.org/10.1137/130931667

A finite element variational multiscale method for steady‐state natural convection problem based on two local gauss integrations

Yunzhang Zhang, Yanren Hou and Haibiao Zheng
Numerical Methods for Partial Differential Equations 30 (2) 361 (2014)
https://doi.org/10.1002/num.21811

On Monotonicity-Preserving Stabilized Finite Element Approximations of Transport Problems

Santiago Badia and Alba Hierro
SIAM Journal on Scientific Computing 36 (6) A2673 (2014)
https://doi.org/10.1137/130927206

The characteristic variational multiscale method for convection-dominated convection–diffusion–reaction problems

Lingzhi Qian, Huiping Cai, Rui Guo and Xinlong Feng
International Journal of Heat and Mass Transfer 72 461 (2014)
https://doi.org/10.1016/j.ijheatmasstransfer.2014.01.020

On the convergence of Variational multiscale methods based on Newton’s iteration for the incompressible flows

Feng Shi, Haibiao Zheng, Jiaping Yu and Ying Li
Applied Mathematical Modelling 38 (23) 5726 (2014)
https://doi.org/10.1016/j.apm.2014.04.049

Variational multiscale proper orthogonal decomposition: Navier‐stokes equations

Traian Iliescu and Zhu Wang
Numerical Methods for Partial Differential Equations 30 (2) 641 (2014)
https://doi.org/10.1002/num.21835

Automatically stable discontinuous Petrov–Galerkin methods for stationary transport problems: Quasi-optimal test space norm

Antti H. Niemi, Nathaniel O. Collier and Victor M. Calo
Computers & Mathematics with Applications 66 (10) 2096 (2013)
https://doi.org/10.1016/j.camwa.2013.07.016

A subgrid stabilization finite element method for incompressible magnetohydrodynamics

Mine A. Belenli, Songül Kaya, Leo G. Rebholz and Nicholas E. Wilson
International Journal of Computer Mathematics 90 (7) 1506 (2013)
https://doi.org/10.1080/00207160.2012.758363

Error analysis of a fully discrete finite element variational multiscale method for time‐dependent incompressible Navier–Stokes equations

Yueqiang Shang
Numerical Methods for Partial Differential Equations 29 (6) 2025 (2013)
https://doi.org/10.1002/num.21787